Proposition 24
Theorem
Similar segments of circles (AEB , CFD ) on equal chords (AB , CD ) are equal.
Commentary
1. Let AB and CD be the given equal chords.
2. LetAEB and CFD be the given similar segments of circles. By definition of similar segments of circles, ∠AEB = ∠CFD .
3. Then the two segments of circlesAEB and CFD are congruent.
4. This proposition is the general case of the previous proposition, Euclid Book 3 Proposition 23, which covers the case of similar segments of circles on the same chord.
2. Let
3. Then the two segments of circles
4. This proposition is the general case of the previous proposition, Euclid Book 3 Proposition 23, which covers the case of similar segments of circles on the same chord.
Original statement
τὰ ἐπὶ ἴσων ϵὐθϵιῶν ὅμοια τμήματα κύκλων ἴσα ἀλλήλοις ἐστίν.
English translation
Similar segments of circles on equal straight lines are equal to one another.
